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Question

The harmonic mean of 2 numbers is 4. Their arithmetic mean A and geometric mean G satisfy the relation 2A + G2 = 27. The sum of the numbers is __

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Solution

Let the numbers be a & b

H = 4

G2 = AH = 4A -------------(1)

Given 2A + G2 = 27 -----------(2)

From (1) & (2)

6A = 27 A = 92

G2 = 4 × 92 = 18

If we know A and G, the 2 numbers are given by,

a, b = A ± A2G2

= 92 ± 81418

= 92 ± 32 = 6, 3 (or) 3, 6

Therefore, the sum of the numbers = 9


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